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We present a certiﬁed reduced basis method for a steady-state quadratically nonlinear diffusion equation. We
employ the standard Galerkin recipe for the reduced basis approximation and derive associated a posteriori error
estimation procedures based on the Brezzi-Rappaz-Raviart (BRR) framework. We show that all necessary ingredients,
i.e., the dual norm of the residual, the Sobolev embedding constant, and a lower bound of the inf-sup constant, can be
decomposed in an offline-online computational decompostion. Numerical results are presented to conﬁrm the rapid
convergence of the reduced basis approximation and the rigor and sharpness of the associated a posteriori error bound.